The 5th KAIST Geometric Topology Fair

A workshop on geometric topology
including knot theory, manifold theory, and related topics

July 31 - August 3, 2006

Busan Youth Hostel Arpina, Heaundea-gu, Busan, Korea

The aim of this workshop is to encourage academic activities in the area of geometric topology in Korea and promote friendly relations between researchers in this area. This year we focus on knot theory and low-dimensional manifolds. We hope this workshop contributes to acceleration of research in this field.

Organizers

Ki Hyoung Ko (KAIST), Gyo Taek Jin (KAIST), and Hun Kim (KAIST)

Confirmed Participants

An, Byoung Hee KAIST
Cha, Jae Choon ICU
Huh, Young Sik Hanyang University
Hwag, Taek Kyu KAIST
Jeon, Choon Bae    Daeduk College
Jin, Gyo Taek KAIST
Kim, Hun KAIST
Kim, Jee Hyoun KAIST
Kim, Jin Hong KAIST
Kim, Min KAIST
Kim, Taehee Konkuk University
         
Ko, Ki Hyoung KAIST
Lee, Hwa Jeong KAIST
Lee, Jae-eun KAIST
Lee, Jang Won KAIST
Lee, Jung Hun KAIST
Lee, Sang Jin Konkuk University
Park, Hyo Won KAIST
Park, Seo Jung KAIST
Song, Won Taek    ICU

Invited speakers

Kent E. Orr    Indiana University
         
Yuanan Diao    University   of   North Carolina

Programs

July 31     Room   4416   Natural Science Building,  KAIST,  Daejeon
PM 03:00-04:20    Kent E. Orr TBA
PM 04:40-06:00 Yuanan Diao Topological and geometrical problems of Random knots
August 2     Busan Youth Hostel Arpina,   Heaundea-gu,   Busan
09:20-09:30 Announcements
09:30-10:10 Kent E. Orr TBA
10:20-11:00 Yuanan Diao Some geometric problems of physical knots I
11:10-11:50 Sang Jin Lee Conjugacy classes in Garside groups
11:50-01:30 --- Lunch ---
01:30-02:10 Kent E. Orr TBA
02:20-03:00 Yuanan Diao Some geometric problems of physical knots II
03:00-03:30 --- Coffee Break ---
03:30-04:10 Jae Choon Cha L^2 signatures and minimal genus in 4-manifolds

Registration

Benefits for registeration include:
  • Participation in the academic programs
  • Rooms in the workshop venue (Busan Youth Hostel Arpina) for two nights, August 1 and 2
  • Dinner on August 1, breakfast and dinner on August 2 and breakfast on August 3 (accompanying people are also welcome)
  • Registration Fee

    Participants accompanied with family 220,000
    Participants not accompanied with family 75,000
    (Korean Won)

    Very limited funding may be available to those not supported by other grants. Please contact the organizers (see the contact information below).

    Accomodations

    We have reserved a block of rooms for participants. We welcome your family; for more comfortable stay, we will assign to each family a guest house with a bedroom and bathroom. Participants not accompanied with family will be asked to share similar guest houses.

    Contact

    For any inquiries on the workshop, please contact:

    Hun Kim
    Korea Advanced Institute of Science and Technology
    373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Korea
    Phone: +82-42-869-8982
    Email: HunKim@kaist.ac.kr

    Local information

    For more information on the hotel, please see the home page of Busan Youth Hostel Arpina (in Korean)

    Abstracts

    Yuanan Diao, Topological and Geometrical Problems of Random Knots

    In this talk, I will give an overview of the various topological and geometrical problems encountered in random knots. I will briefly discuss several commonly used random knot models, state the problems and present some theoretical as well as numerical results. At the end, I will discuss the random knotting and linking problem in a confined space.

    Yuanan Diao, Some Geometric Problems of Physical Knots I

    In this talk, I will mainly address some geometric problems associated with the ropelength of a physical knot, that is, a knot realized with a rope of certain thickness. In particular, I will discuss the global ropelength lower bound for any non-trivial knot, the general ropelength lower bound for a non-trivial knot in terms of its crossing number, and the general ropelength upper bound for a non-trivial knot in terms of its crossing number.

    Yuanan Diao, Some Geometric Problems of Physical Knots II

    In this talk, I will continue the topics discussed in the first part. I will discuss several approaches aimed to improve the general ropelength upper bound of a knot and present some results. Some numerical results about the ropelength of physical knots will also be presented. At the end, I will discuss some recent results regarding the total curvature of physical knots.

    Sang Jin Lee , Conjugacy classes in Garside groups

    The Garside group is a lattice-theoretic generalization of braid groups and Artin groups of finite type. We will talk about the notion of Garside groups and the structure of conjugacy classes, and discuss the asymptotic behavior of infimum under taking power and the applications of this results. If time allowed, some related results will also be discussed.